Bulk Capacitor Hold-Up Energy
E = 0.5 × C × (V1² − V2²)
Quick answer
This calculator solves E = 0.5 × C × (V1² − V2²) for Capacitance. With Available Energy 100 mJ, Initial Voltage 12 V, Final Voltage 26.4 V, the result is -0.3617 mF.
Calculator
Formula
Description
Bulk capacitors provide energy during brief power interruptions or load transients. The usable energy is not the total stored energy but only the difference between the energy at the starting voltage and the energy at the minimum acceptable voltage. A capacitor charged to 12V that can discharge to 10V provides only 36% of its total stored energy. This formula is essential for sizing hold-up capacitors in power supplies, ride-through capacitors for motor drives, and energy storage for peak load handling.
Variables
- E — Usable energy between V1 and V2 (J)
- C — Capacitance (F)
- V1 — Initial (fully charged) voltage (V)
- V2 — Minimum acceptable voltage (V)
Practical Notes
Hold-up time = E / P_load. For a 20W load requiring 20ms hold-up from 12V to 10V: C = 2 × 0.020 × 20 / (144 - 100) = 18.2 mF. Use electrolytic or supercapacitors for bulk energy storage. Account for capacitor aging (electrolytic capacitors lose 20-30% capacitance over their lifetime) and temperature derating.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| E | Available Energy | mJ | µJ, mJ, J, kJ, Wh, kWh |
| C | Capacitance | µF | pF, nF, µF, mF, F |
| V1 | Initial Voltage | V | pV, nV, µV, mV, V, kV |
| V2 | Final Voltage | V | pV, nV, µV, mV, V, kV |
Step by step
- 1. What you know: Available Energy 100 mJ, Initial Voltage 12 V, Final Voltage 26.4 V
- 2. The relation: E = 0.5 × C × (V1² − V2²)
- 3. Substitute: E = 100 mJ, V1 = 12 V, V2 = 26.4 V
- 4. Result: Capacitance = -0.3617 mF
Worked examples
Minimum range
Given: Available Energy 100 µJ, Initial Voltage 0.33 V, Final Voltage 0.726 V
Result: Capacitance = -0.4783 mF
Low range
Given: Available Energy 1 mJ, Initial Voltage 3.3 V, Final Voltage 7.26 V
Result: Capacitance = -47.83 µF
Typical
Given: Available Energy 100 mJ, Initial Voltage 12 V, Final Voltage 26.4 V
Result: Capacitance = -0.3617 mF
High range
Given: Available Energy 1 J, Initial Voltage 0.23 kV, Final Voltage 0.506 kV
Result: Capacitance = -9.846 µF
Maximum range
Given: Available Energy 10 J, Initial Voltage 2.3 kV, Final Voltage 5.06 kV
Result: Capacitance = -0.9846 µF
How Capacitance changes with Available Energy
| Available Energy (input) | Capacitance (result) |
|---|---|
| 10 mJ | -36.17 µF |
| 25 mJ | -90.42 µF |
| 50 mJ | -0.1808 mF |
| 75 mJ | -0.2713 mF |
| 100 mJ | -0.3617 mF |
| 150 mJ | -0.5425 mF |
| 0.2 J | -0.7234 mF |
| 0.4 J | -1.447 mF |
| 0.7 J | -2.532 mF |
| 1 J | -3.617 mF |
The same result in other units
| Unit | Value |
|---|---|
| nF | -361700 |
| µF | -361.7 |
| mF | -0.3617 |
| F | -0.0003617 |
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<p><a href="https://vbatpower.com/formulas/bulk-cap-energy/">Bulk Capacitor Hold-Up Energy</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Bulk Capacitor Hold-Up Energy?
Use E = 0.5 × C × (V1² − V2²). With Available Energy 100 mJ, Initial Voltage 12 V, Final Voltage 26.4 V, Capacitance works out to -0.3617 mF.
How do you calculate capacitor value to hold up 0.4a at 12v for 20ms?
Rearrange for Capacitance: with Available Energy 1 mJ, Initial Voltage 3.3 V, Final Voltage 7.26 V, Capacitance is -47.83 µF.
What is the formula for Bulk Capacitor Hold-Up Energy?
The formula is E = 0.5 × C × (V1² − V2²). Bulk capacitors provide energy during brief power interruptions or load transients.
What units does Bulk Capacitor Hold-Up Energy use?
Capacitance is shown in nF, µF, mF, F. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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